On January 12, 2010, a magnitude 7.0 earthquake struck Haiti causing significant damage which affected approximately 3 million citizens. In the wake of the disaster, aid groups were working to locate displaced persons and provide them with food and water. However, due to the large scale destruction of infrastructure over a wide area additional assistance was needed to locate people quickly.
Little is left of a neighborhood on a hillside near downtown Port-au-Prince on Jan. 15. More than a million people were displaced by the quake. (David Gilkey/NPR)
Displaced persons were known to be making make-shift shelters out of blue tarps. High resolution geo-refereneced images were captured by aircraft of the destroyed areas. The data generated by the image collection was too large for aid workers to process in time to supply aid. Therefore, a team from the Rochester Institute of Technology used data-mining algorithms to analyze the images and identify blue tarps. The goal was to effectively locate displaced persons and communicate their location to rescue workers so they could get resources to people who needed it in time.
Sample image of a geo-referenced image used for the analysis
As the final project for SYS 6018 - Data Mining, we were assigned to build models from the different techniques we learned in the course to, as accurately as possible, and in as timely a manner as possible, locate as many of the displaced persons identified in the imagery data so that they could be provided food and water before their situations became unsurvivable. The data made available to students consisted of a csv of red, green, blue pixel values and a class indicator which indicated if a pixel was representative of a blue tarp or something else like vegetation. A final hold-out data set presented in the format of multiple text files was provided as well.
The US Government spent $1.5B on Haiti disaster relief by the end of 2010.
The data provided for analysis was generated from overhead images and stored as a three channel output. Each pixel also had a classifier label indicating whether it was a blue tarp or something else like vegetation or soil. The channels represented the red, green, and blue values for pixels within images. RGB color model is referred to as an additive model. The integer value for the red, green, and blue channels are combined to represent a color. Typically, the component values are stored as an 8 bit integer ranging from 0 to 255.
df <- tibble(read.csv("HaitiPixels.csv")) #read in df
"Check for NA values"
anyNA(df) #check for NA values
"Summary of Data"
summary(df) #quick look at data
df$Class <- factor(df$Class) #make Class a factor variable.
#> [1] "Check for NA values"
#> [1] FALSE
#> [1] "Summary of Data"
#> Class Red Green Blue
#> Length:63241 Min. : 48 Min. : 48.0 Min. : 44.0
#> Class :character 1st Qu.: 80 1st Qu.: 78.0 1st Qu.: 63.0
#> Mode :character Median :163 Median :148.0 Median :123.0
#> Mean :163 Mean :153.7 Mean :125.1
#> 3rd Qu.:255 3rd Qu.:226.0 3rd Qu.:181.0
#> Max. :255 Max. :255.0 Max. :255.0
#Reference [1]
# The palette with grey:
cbPalette <- c("#999999", "#E69F00", "#56B4E9", "#009E73", "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
# To use for fills, add
#scale_fill_manual(values=cbPalette)
ggpairs(df[,2:4], lower.panel = NULL, upper = list(continuous = wrap("cor", size = 3)), aes(color=df$Class))# + scale_fill_manual(values=cbPalette)
#view scatter and correlations
attach(df) #attach df variables
fig <- plot_ly(df, x=~Red, y=~Green, z=~Blue, color=~Class) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig <- fig %>% add_markers()
fig <- fig %>% layout(scene=list(xaxis=list(title="Red"),
yaxis = list(title = 'Green'),
zaxis = list(title = 'Blue')))
fig
!!!!!!!!!! IF I HAVE TIME MAKE A SELECTOR TO CHOOSE COLOR SCHEME FOR NOT COLOR BLIND OR DIFFERENT KINDS OF COLOR BLIND https://socviz.co/refineplots.html
Initial inspection of the data frame indicated no missing values. The data provided is sufficiently cleaned only one further adjustment to the data frame is needed. Since our main interest is to predict whether a pixel represents a blue tarp or not a blue tarp, the Class column of the data frame needs to be converted into a binary indicator for blue tarp or not blue tarp. This is done in the next section.
The data was visualized with the ggpairs function. For a pair of variables chosen from the data frame, Ggpairs generates a scatterplot, displays a Pearson correlation, and, on the diagonal, shows a variable distribution. The plots were also color-coded by class. The class label describes what kind of object a pixel is associated with. In our data frame there were the following classes: Blue Tarp, Rooftop, Soil, Various Non-tarp, and Vegetation. The 2D representation of the data only gives us a partial insight into the behavior and relationships of the predictors. Since three channels are used to generate a color, plotting the data in 3D to investigate trends and behavior between classes will be more meaningful.
The 3D scatter plot shows a significant amount of overlap between the different classes. It is worth noting that it is possible to see some separation between the classes.
df <- cbind(mutate(df, "Blue_Tarp_or_Not"=ifelse(Class != "Blue Tarp", 0, 1))) #add binary column indicating whether the Class variable is "Blue Tarp" or not
attach(df)
df$Blue_Tarp_or_Not <- factor(Blue_Tarp_or_Not, labels = c("NBT", "BT"))#, levels =c(0,1), labels = c("NBT", "BT")) #ensure new column is a factor
"First Six Rows of Data Frame"
head(df)
df_factor <- df[, -1]
"Last Six Rows of Data Frame"
tail(df_factor)
attach(df_factor)
#> [1] "First Six Rows of Data Frame"
#> Class Red Green Blue Blue_Tarp_or_Not
#> 1 Vegetation 64 67 50 NBT
#> 2 Vegetation 64 67 50 NBT
#> 3 Vegetation 64 66 49 NBT
#> 4 Vegetation 75 82 53 NBT
#> 5 Vegetation 74 82 54 NBT
#> 6 Vegetation 72 76 52 NBT
#> [1] "Last Six Rows of Data Frame"
#> Red Green Blue Blue_Tarp_or_Not
#> 63236 136 145 150 BT
#> 63237 138 146 150 BT
#> 63238 134 141 152 BT
#> 63239 136 143 151 BT
#> 63240 132 139 149 BT
#> 63241 133 141 153 BT
fig1 <- plot_ly(df_factor, x=~Red, y=~Green, z=~Blue, color=~Blue_Tarp_or_Not) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig1 <- fig1 %>% add_markers()
fig1 <- fig1 %>% layout(scene=list(xaxis=list(title="Red"),
yaxis = list(title = 'Green'),
zaxis = list(title = 'Blue')))
fig1
After the class label is converted into a binary classifier, it is easier to see separation between the data points for blue tarps and not blue tarps.
#In order to make run times faster when tuning parameters subset data with 20%
trainIndex <- createDataPartition(df_factor$Blue_Tarp_or_Not, p=0.2,
list=FALSE,
times=1)
df_subset <- df_factor[trainIndex,]
Fit a Logistic Regression Model !!!Need to turn on the fold result saving …
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
glm.fit <- caret::train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,
method="glm",
family="binomial",
trControl= fitControl)
glm.fit
"Summary"
summary(glm.fit)
#> Generalized Linear Model
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> No pre-processing
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results:
#>
#> Accuracy Kappa
#> 0.9954936 0.9243199
#>
#> [1] "Summary"
#>
#> Call:
#> NULL
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -2.7624 -0.0205 -0.0014 0.0000 3.2666
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) 0.15533 0.40656 0.382 0.702
#> Red -0.26031 0.02712 -9.597 < 2e-16 ***
#> Green -0.21780 0.02892 -7.532 4.99e-14 ***
#> Blue 0.47311 0.03355 14.101 < 2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 3584.46 on 12648 degrees of freedom
#> Residual deviance: 352.83 on 12645 degrees of freedom
#> AIC: 360.83
#>
#> Number of Fisher Scoring iterations: 12
Test model performance on Train data to select threshold values…
#pass
glm.prob <- predict(glm.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
glm_roc <- roc(df_subset $Blue_Tarp_or_Not, glm.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="GLM ROC Curve")
roc.info_glm <- roc(df_subset$Blue_Tarp_or_Not, glm.prob[,2], legacy.axes=TRUE)
roc.glm.df <- data.frame(tpp=roc.info_glm$sensitivities*100, fpp=(1-roc.info_glm$specificities)*100, thresholds=roc.info_glm$thresholds)
#roc.glm.df[roc.glm.df>98.5 & roc.glm.df < 99,]
glm.thresholds <- data.matrix(roc.glm.df$thresholds)
fig2 <- plot_ly(roc.glm.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig2 <- fig2 %>% add_markers()
fig2 <- fig2 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig2
lr.thresh <- 0.5
glm.pred_thresh <- factor(ifelse(glm.prob[,2]>lr.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.glm_thresh <- confusionMatrix(factor(glm.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.glm_thresh
acc_LR <- cm.glm_thresh[["overall"]][["Accuracy"]]*100
auc_LR <- glm_roc[["auc"]]
thresh_LR <- lr.thresh
sens_LR <- cm.glm_thresh[["byClass"]][["Sensitivity"]]*100
spec_LR <- cm.glm_thresh[["byClass"]][["Specificity"]]*100
FDR_LR <- ((cm.glm_thresh[["table"]][2,1])/(cm.glm_thresh[["table"]][2,1]+cm.glm_thresh[["table"]][2,2]))*100
prec_LR <- cm.glm_thresh[["byClass"]][["Precision"]]*100
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12231 43
#> BT 13 362
#>
#> Accuracy : 0.9956
#> 95% CI : (0.9943, 0.9967)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2.2e-16
#>
#> Kappa : 0.9259
#>
#> Mcnemar's Test P-Value : 0.0001065
#>
#> Sensitivity : 0.89383
#> Specificity : 0.99894
#> Pos Pred Value : 0.96533
#> Neg Pred Value : 0.99650
#> Prevalence : 0.03202
#> Detection Rate : 0.02862
#> Detection Prevalence : 0.02965
#> Balanced Accuracy : 0.94638
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
glm.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
glm.sd <- sd(glm.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa parameter Resample
#> 1 0.9944664 0.9128059 none Fold01
#> 2 0.9952532 0.9164905 none Fold02
#> 3 0.9944664 0.9085369 none Fold03
#> 4 0.9944708 0.9107247 none Fold04
#> 5 0.9960506 0.9330371 none Fold05
#> 6 0.9968379 0.9470911 none Fold06
#> 7 0.9952569 0.9225526 none Fold07
#> 8 0.9944620 0.9012853 none Fold08
#> 9 0.9952532 0.9164905 none Fold09
#> 10 0.9984190 0.9741842 none Fold10
The average accuracy across ten folds is 99.56 with a standard deviation of 0.129.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
lda.fit <- caret::train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="lda",
verbose= FALSE,
trControl= fitControl)
lda.fit
"Summary"
summary(lda.fit)
#> Linear Discriminant Analysis
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results:
#>
#> Accuracy Kappa
#> 0.9848994 0.7665355
#>
#> [1] "Summary"
#> Length Class Mode
#> prior 2 -none- numeric
#> counts 2 -none- numeric
#> means 6 -none- numeric
#> scaling 3 -none- numeric
#> lev 2 -none- character
#> svd 1 -none- numeric
#> N 1 -none- numeric
#> call 4 -none- call
#> xNames 3 -none- character
#> problemType 1 -none- character
#> tuneValue 1 data.frame list
#> obsLevels 2 -none- character
#> param 1 -none- list
#pass
lda.prob <- predict(lda.fit, newdata=df_subset, type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
lda_roc <- roc(df_subset$Blue_Tarp_or_Not, lda.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="LDA ROC Curve")
roc.info_lda <- roc(df_subset $Blue_Tarp_or_Not, lda.prob[,2], legacy.axes=TRUE)
roc.lda.df <- data.frame(tpp=roc.info_lda$sensitivities*100, fpp=(1-roc.info_lda$specificities)*100, thresholds=roc.info_lda$thresholds)
#roc.lda.df[roc.lda.df>91.5 & roc.lda.df < 91.6,]
fig3 <- plot_ly(roc.lda.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig3 <- fig3 %>% add_markers()
fig3 <- fig3 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig3
lda.thresh <- 0.5
lda.pred_thresh <- factor(ifelse(lda.prob[,2]>lda.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.lda_thresh <- confusionMatrix(factor(lda.pred_thresh),df_subset$Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.lda_thresh
acc_lda <- cm.lda_thresh[["overall"]][["Accuracy"]]*100
auc_lda <- lda_roc[["auc"]]
thresh_lda <- lr.thresh
sens_lda <- cm.lda_thresh[["byClass"]][["Sensitivity"]]*100
spec_lda <- cm.lda_thresh[["byClass"]][["Specificity"]]*100
FDR_lda <- ((cm.lda_thresh[["table"]][2,1])/(cm.lda_thresh[["table"]][2,1]+cm.lda_thresh[["table"]][2,2]))*100
prec_lda <- cm.lda_thresh[["byClass"]][["Precision"]]*100
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12131 77
#> BT 113 328
#>
#> Accuracy : 0.985
#> 95% CI : (0.9827, 0.987)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2e-16
#>
#> Kappa : 0.7677
#>
#> Mcnemar's Test P-Value : 0.01111
#>
#> Sensitivity : 0.80988
#> Specificity : 0.99077
#> Pos Pred Value : 0.74376
#> Neg Pred Value : 0.99369
#> Prevalence : 0.03202
#> Detection Rate : 0.02593
#> Detection Prevalence : 0.03486
#> Balanced Accuracy : 0.90032
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
lda.fit$resample
lda.sd <- sd(lda.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa parameter Resample
#> 1 0.9849802 0.7687274 none Fold01
#> 2 0.9762658 0.6469011 none Fold02
#> 3 0.9865613 0.7976857 none Fold03
#> 4 0.9834123 0.7500611 none Fold04
#> 5 0.9865719 0.7882402 none Fold05
#> 6 0.9873518 0.8074215 none Fold06
#> 7 0.9849802 0.7517533 none Fold07
#> 8 0.9841772 0.7592931 none Fold08
#> 9 0.9865506 0.7778697 none Fold09
#> 10 0.9881423 0.8174023 none Fold10
The average accuracy across ten folds is 98.5 with a standard deviation of 0.337.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
qda.fit <- caret::train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="qda",
verbose= FALSE,
trControl= fitControl)
qda.fit
"Summary"
summary(qda.fit)
#> Quadratic Discriminant Analysis
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results:
#>
#> Accuracy Kappa
#> 0.9946238 0.9050265
#>
#> [1] "Summary"
#> Length Class Mode
#> prior 2 -none- numeric
#> counts 2 -none- numeric
#> means 6 -none- numeric
#> scaling 18 -none- numeric
#> ldet 2 -none- numeric
#> lev 2 -none- character
#> N 1 -none- numeric
#> call 4 -none- call
#> xNames 3 -none- character
#> problemType 1 -none- character
#> tuneValue 1 data.frame list
#> obsLevels 2 -none- character
#> param 1 -none- list
#pass
qda.prob <- predict(qda.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
qda_roc <- roc(df_subset $Blue_Tarp_or_Not, qda.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="QDA ROC Curve")
roc.info_qda <- roc(df_subset$Blue_Tarp_or_Not, qda.prob[,2], legacy.axes=TRUE)
roc.qda.df <- data.frame(tpp=roc.info_qda$sensitivities*100, fpp=(1-roc.info_qda$specificities)*100, thresholds=roc.info_qda$thresholds)
#roc.qda.df[roc.qda.df>98 & roc.qda.df < 99,]
fig4 <- plot_ly(roc.qda.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig4 <- fig4 %>% add_markers()
fig4 <- fig4 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig4
qda.thresh <- 0.5
qda.pred_thresh <- factor(ifelse(qda.prob[,2]>qda.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.qda_thresh <- confusionMatrix(factor(qda.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.qda_thresh
acc_qda <- cm.qda_thresh[["overall"]][["Accuracy"]]*100
auc_qda <- qda_roc[["auc"]]
thresh_qda <- lr.thresh
sens_qda <- cm.qda_thresh[["byClass"]][["Sensitivity"]]*100
spec_qda <- cm.qda_thresh[["byClass"]][["Specificity"]]*100
FDR_qda <- ((cm.qda_thresh[["table"]][2,1])/(cm.qda_thresh[["table"]][2,1]+cm.qda_thresh[["table"]][2,2]))*100
prec_qda <- cm.qda_thresh[["byClass"]][["Precision"]]*100
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12243 67
#> BT 1 338
#>
#> Accuracy : 0.9946
#> 95% CI : (0.9932, 0.9958)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2.2e-16
#>
#> Kappa : 0.9059
#>
#> Mcnemar's Test P-Value : 3.211e-15
#>
#> Sensitivity : 0.83457
#> Specificity : 0.99992
#> Pos Pred Value : 0.99705
#> Neg Pred Value : 0.99456
#> Prevalence : 0.03202
#> Detection Rate : 0.02672
#> Detection Prevalence : 0.02680
#> Balanced Accuracy : 0.91724
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
qda.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
qda.sd <- sd(qda.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa parameter Resample
#> 1 0.9968379 0.9457431 none Fold01
#> 2 0.9912975 0.8362231 none Fold02
#> 3 0.9952569 0.9186146 none Fold03
#> 4 0.9944708 0.9038432 none Fold04
#> 5 0.9944708 0.9038432 none Fold05
#> 6 0.9952569 0.9186234 none Fold06
#> 7 0.9952569 0.9186234 none Fold07
#> 8 0.9952532 0.9164905 none Fold08
#> 9 0.9928797 0.8696370 none Fold09
#> 10 0.9952569 0.9186234 none Fold10
The average accuracy across ten folds is 99.46 with a standard deviation of 0.153.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
knn.fit <- train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="knn",
trControl= fitControl,
tuneLength=5
)
knn.fit
"Summary"
summary(knn.fit)
#> k-Nearest Neighbors
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results across tuning parameters:
#>
#> k Accuracy Kappa
#> 5 0.9961258 0.9368764
#> 7 0.9959676 0.9336437
#> 9 0.9957305 0.9297356
#> 11 0.9957305 0.9296489
#> 13 0.9953351 0.9227537
#>
#> Accuracy was used to select the optimal model using the largest value.
#> The final value used for the model was k = 5.
#> [1] "Summary"
#> Length Class Mode
#> learn 2 -none- list
#> k 1 -none- numeric
#> theDots 0 -none- list
#> xNames 3 -none- character
#> problemType 1 -none- character
#> tuneValue 1 data.frame list
#> obsLevels 2 -none- character
#> param 0 -none- list
#pass
knn.prob <- predict(knn.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
knn_roc <- roc(df_subset $Blue_Tarp_or_Not, knn.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="KNN ROC Curve")
Not sure why there are only 10 values for this one…?
roc.info_knn <- roc(df_subset$Blue_Tarp_or_Not, knn.prob[,2], legacy.axes=TRUE)
roc.knn.df <- data.frame(tpp=roc.info_knn$sensitivities*100, fpp=(1-roc.info_knn$specificities)*100, thresholds=roc.info_knn$thresholds)
#roc.knn.df[roc.knn.df>99 & roc.knn.df < 100,]
#roc.knn.df
fig5 <- plot_ly(roc.knn.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig5 <- fig5 %>% add_markers()
fig5 <- fig5 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig5
knn.thresh <- 0.5
knn.pred_thresh <- factor(ifelse(knn.prob[,2]>knn.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.knn_thresh <- confusionMatrix(factor(knn.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.knn_thresh
acc_knn <- cm.knn_thresh[["overall"]][["Accuracy"]]*100
auc_knn <- knn_roc[["auc"]]
thresh_knn <- lr.thresh
sens_knn <- cm.knn_thresh[["byClass"]][["Sensitivity"]]*100
spec_knn <- cm.knn_thresh[["byClass"]][["Specificity"]]*100
FDR_knn <- ((cm.knn_thresh[["table"]][2,1])/(cm.knn_thresh[["table"]][2,1]+cm.knn_thresh[["table"]][2,2]))*100
prec_knn <- cm.knn_thresh[["byClass"]][["Precision"]]*100
k_knn <- knn.fit[["bestTune"]][["k"]]
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12230 17
#> BT 14 388
#>
#> Accuracy : 0.9975
#> 95% CI : (0.9965, 0.9983)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : <2e-16
#>
#> Kappa : 0.9603
#>
#> Mcnemar's Test P-Value : 0.7194
#>
#> Sensitivity : 0.95802
#> Specificity : 0.99886
#> Pos Pred Value : 0.96517
#> Neg Pred Value : 0.99861
#> Prevalence : 0.03202
#> Detection Rate : 0.03067
#> Detection Prevalence : 0.03178
#> Balanced Accuracy : 0.97844
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
knn.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
knn.sd <- sd(knn.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa k Resample
#> 1 0.9944664 0.9128059 5 Fold01
#> 2 0.9944664 0.9107224 7 Fold01
#> 3 0.9944664 0.9107224 9 Fold01
#> 4 0.9944664 0.9107224 11 Fold01
#> 5 0.9936759 0.8967347 13 Fold01
#> 6 0.9920886 0.8677160 5 Fold02
#> 7 0.9905063 0.8372253 7 Fold02
#> 8 0.9905063 0.8372253 9 Fold02
#> 9 0.9897152 0.8258732 11 Fold02
#> 10 0.9889241 0.8100962 13 Fold02
#> 11 0.9952569 0.9243798 5 Fold03
#> 12 0.9968379 0.9483673 7 Fold03
#> 13 0.9960474 0.9346692 9 Fold03
#> 14 0.9960474 0.9346692 11 Fold03
#> 15 0.9952569 0.9225510 13 Fold03
#> 16 0.9952607 0.9243803 5 Fold04
#> 17 0.9944708 0.9128048 7 Fold04
#> 18 0.9944708 0.9128048 9 Fold04
#> 19 0.9944708 0.9128048 11 Fold04
#> 20 0.9944708 0.9128048 13 Fold04
#> 21 0.9984202 0.9741849 5 Fold05
#> 22 0.9984202 0.9741849 7 Fold05
#> 23 0.9984202 0.9741849 9 Fold05
#> 24 0.9984202 0.9741849 11 Fold05
#> 25 0.9984202 0.9741849 13 Fold05
#> 26 0.9984190 0.9741842 5 Fold06
#> 27 0.9968379 0.9495855 7 Fold06
#> 28 0.9976285 0.9617382 9 Fold06
#> 29 0.9984190 0.9741842 11 Fold06
#> 30 0.9984190 0.9741842 13 Fold06
#> 31 0.9968379 0.9483684 5 Fold07
#> 32 0.9976285 0.9608031 7 Fold07
#> 33 0.9960474 0.9346719 9 Fold07
#> 34 0.9952569 0.9206366 11 Fold07
#> 35 0.9952569 0.9206366 13 Fold07
#> 36 0.9960443 0.9330281 5 Fold08
#> 37 0.9960443 0.9330281 7 Fold08
#> 38 0.9960443 0.9346675 9 Fold08
#> 39 0.9960443 0.9330281 11 Fold08
#> 40 0.9960443 0.9330281 13 Fold08
#> 41 0.9968354 0.9470864 5 Fold09
#> 42 0.9968354 0.9470864 7 Fold09
#> 43 0.9968354 0.9470864 9 Fold09
#> 44 0.9976266 0.9608005 11 Fold09
#> 45 0.9968354 0.9470864 13 Fold09
#> 46 0.9976285 0.9626296 5 Fold10
#> 47 0.9976285 0.9626296 7 Fold10
#> 48 0.9968379 0.9495855 9 Fold10
#> 49 0.9968379 0.9495855 11 Fold10
#> 50 0.9960474 0.9362303 13 Fold10
The average accuracy across ten folds when k = 5 is 99.75 with a standard deviation of 0.229.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
rf.fit <- train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="rf", #what is the difference between the different caret rf models??
trControl= fitControl,
tuneLength=3
)
rf.fit
"Summary"
summary(rf.fit)
#> note: only 2 unique complexity parameters in default grid. Truncating the grid to 2 .
#>
#> Random Forest
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results across tuning parameters:
#>
#> mtry Accuracy Kappa
#> 2 0.9958096 0.9315366
#> 3 0.9958097 0.9315412
#>
#> Accuracy was used to select the optimal model using the largest value.
#> The final value used for the model was mtry = 3.
#> [1] "Summary"
#> Length Class Mode
#> call 4 -none- call
#> type 1 -none- character
#> predicted 12649 factor numeric
#> err.rate 1500 -none- numeric
#> confusion 6 -none- numeric
#> votes 25298 matrix numeric
#> oob.times 12649 -none- numeric
#> classes 2 -none- character
#> importance 3 -none- numeric
#> importanceSD 0 -none- NULL
#> localImportance 0 -none- NULL
#> proximity 0 -none- NULL
#> ntree 1 -none- numeric
#> mtry 1 -none- numeric
#> forest 14 -none- list
#> y 12649 factor numeric
#> test 0 -none- NULL
#> inbag 0 -none- NULL
#> xNames 3 -none- character
#> problemType 1 -none- character
#> tuneValue 1 data.frame list
#> obsLevels 2 -none- character
#> param 0 -none- list
#pass
RF.prob <- predict(rf.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
RF_roc <- roc(df_subset $Blue_Tarp_or_Not, RF.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="RF ROC Curve")
roc.info_rf <- roc(df_subset$Blue_Tarp_or_Not, RF.prob[,2], legacy.axes=TRUE)
roc.rf.df <- data.frame(tpp=roc.info_rf$sensitivities*100, fpp=(1-roc.info_rf$specificities)*100, thresholds=roc.info_rf$thresholds)
#roc.rf.df[roc.rf.df>99 & roc.rf.df < 100,]
#roc.rf.df
fig6 <- plot_ly(roc.rf.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig6 <- fig6 %>% add_markers()
fig6 <- fig6 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig6
RF.thresh <- 0.5
RF.pred_thresh <- factor(ifelse(RF.prob[,2]>RF.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.RF_thresh <- confusionMatrix(factor(RF.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.RF_thresh
acc_RF <- cm.RF_thresh[["overall"]][["Accuracy"]]*100
auc_RF <- RF_roc[["auc"]]
thresh_RF <- lr.thresh
sens_RF <- cm.RF_thresh[["byClass"]][["Sensitivity"]]*100
spec_RF <- cm.RF_thresh[["byClass"]][["Specificity"]]*100
FDR_RF <- ((cm.RF_thresh[["table"]][2,1])/(cm.RF_thresh[["table"]][2,1]+cm.RF_thresh[["table"]][2,2]))*100
prec_RF <- cm.RF_thresh[["byClass"]][["Precision"]]*100
mtry_best <- rf.fit[["bestTune"]][["mtry"]]
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12244 4
#> BT 0 401
#>
#> Accuracy : 0.9997
#> 95% CI : (0.9992, 0.9999)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : <2e-16
#>
#> Kappa : 0.9949
#>
#> Mcnemar's Test P-Value : 0.1336
#>
#> Sensitivity : 0.99012
#> Specificity : 1.00000
#> Pos Pred Value : 1.00000
#> Neg Pred Value : 0.99967
#> Prevalence : 0.03202
#> Detection Rate : 0.03170
#> Detection Prevalence : 0.03170
#> Balanced Accuracy : 0.99506
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
rf.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
rf.sd <- sd(rf.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa mtry Resample
#> 1 0.9944664 0.9128059 2 Fold01
#> 2 0.9944664 0.9128059 3 Fold01
#> 3 0.9920886 0.8643544 2 Fold02
#> 4 0.9936709 0.8914835 3 Fold02
#> 5 0.9976285 0.9617382 2 Fold03
#> 6 0.9968379 0.9483673 3 Fold03
#> 7 0.9936809 0.8991737 2 Fold04
#> 8 0.9944708 0.9107247 3 Fold04
#> 9 0.9984202 0.9741849 2 Fold05
#> 10 0.9976303 0.9608041 3 Fold05
#> 11 0.9976285 0.9626296 2 Fold06
#> 12 0.9976285 0.9626296 3 Fold06
#> 13 0.9952569 0.9225526 2 Fold07
#> 14 0.9952569 0.9225526 3 Fold07
#> 15 0.9952532 0.9206296 2 Fold08
#> 16 0.9952532 0.9206296 3 Fold08
#> 17 0.9960443 0.9346675 2 Fold09
#> 18 0.9960443 0.9346675 3 Fold09
#> 19 0.9976285 0.9626296 2 Fold10
#> 20 0.9968379 0.9507466 3 Fold10
The average accuracy across ten folds when mtry = 3 is 99.97 with a standard deviation of 0.17.
#pass
fitControl <- trainControl(method = "cv",
number = 10,
returnResamp = 'all',
savePredictions = 'final',
classProbs = TRUE)
set.seed(4)
svm.radial.fit <- train(Blue_Tarp_or_Not~Red+Green+Blue,
data = df_subset, #df_factor,,
preProcess=c("center","scale"),
method="svmRadial",
trControl= fitControl,
tuneLength=10
#tuneGrid = expand.grid(C=seq(0,10, length=10),
# sigma =seq(0,10, length=10))
)
svm.radial.fit
"Summary"
summary(svm.radial.fit)
#> Support Vector Machines with Radial Basis Function Kernel
#>
#> 12649 samples
#> 3 predictor
#> 2 classes: 'NBT', 'BT'
#>
#> Pre-processing: centered (3), scaled (3)
#> Resampling: Cross-Validated (10 fold)
#> Summary of sample sizes: 11384, 11385, 11384, 11383, 11383, 11384, ...
#> Resampling results across tuning parameters:
#>
#> C Accuracy Kappa
#> 0.25 0.9958886 0.9316138
#> 0.50 0.9958886 0.9313102
#> 1.00 0.9960467 0.9339361
#> 2.00 0.9962838 0.9380377
#> 4.00 0.9963629 0.9395397
#> 8.00 0.9962838 0.9380981
#> 16.00 0.9963628 0.9393495
#> 32.00 0.9964420 0.9409942
#> 64.00 0.9961258 0.9359431
#> 128.00 0.9962048 0.9373344
#>
#> Tuning parameter 'sigma' was held constant at a value of 8.17509
#> Accuracy was used to select the optimal model using the largest value.
#> The final values used for the model were sigma = 8.17509 and C = 32.
#> [1] "Summary"
#> Length Class Mode
#> 1 ksvm S4
Both linear and poly SVM functions were considered. Radial SVM produced the highest accuracy values of the three methods. SVM radial was chosen for building the SVM model.
#pass
SVM.prob <- predict(svm.radial.fit, newdata=df_subset , type = "prob") #returns df with col 0 (prob not blue tarp) and 1 (prob blue tarp)
par(pty="s")
SVM_roc <- roc(df_subset $Blue_Tarp_or_Not, SVM.prob[,2], plot=TRUE, legacy.axes=TRUE, percent=TRUE, xlab="False Positive Percentage", ylab="True Positive Percentage", col="#965fd4", lwd=4, print.auc=TRUE, main="SVM ROC Curve")
roc.info_svm <- roc(df_subset$Blue_Tarp_or_Not, SVM.prob[,2], legacy.axes=TRUE)
roc.svm.df <- data.frame(tpp=roc.info_svm$sensitivities*100, fpp=(1-roc.info_svm$specificities)*100, thresholds=roc.info_svm$thresholds)
#roc.svm.df[roc.svm.df>99 & roc.svm.df < 100,]
#roc.svm.df
fig7 <- plot_ly(roc.svm.df, x=~tpp, y=~fpp, z=~thresholds) #Reference: https://plotly.com/r/3d-scatter-plots/ https://plotly.com/r/3d-surface-plots/
fig7 <- fig7 %>% add_markers()
fig7 <- fig7 %>% layout(scene=list(xaxis=list(title="True Positive Rate"),
yaxis = list(title = 'False Positive Rate'),
zaxis = list(title = 'Threshold')))
fig7
SVM.thresh <- 0.5
SVM.pred_thresh <- factor(ifelse(SVM.prob[,2]>SVM.thresh,"BT", "NBT"), levels=c("NBT", "BT"))
cm.SVM_thresh <- confusionMatrix(factor(SVM.pred_thresh),df_subset $Blue_Tarp_or_Not, positive = "BT")
"Threshold: 0.5"
cm.SVM_thresh
acc_SVM <- cm.SVM_thresh[["overall"]][["Accuracy"]]*100
auc_SVM <- SVM_roc[["auc"]]
thresh_SVM <- lr.thresh
sens_SVM <- cm.SVM_thresh[["byClass"]][["Sensitivity"]]*100
spec_SVM <- cm.SVM_thresh[["byClass"]][["Specificity"]]*100
FDR_SVM <- ((cm.SVM_thresh[["table"]][2,1])/(cm.SVM_thresh[["table"]][2,1]+cm.SVM_thresh[["table"]][2,2]))*100
prec_SVM <- cm.SVM_thresh[["byClass"]][["Precision"]]*100
#sigma_best <- fill this in after best svm model chosen
#C_best
#> [1] "Threshold: 0.5"
#> Confusion Matrix and Statistics
#>
#> Reference
#> Prediction NBT BT
#> NBT 12234 22
#> BT 10 383
#>
#> Accuracy : 0.9975
#> 95% CI : (0.9964, 0.9983)
#> No Information Rate : 0.968
#> P-Value [Acc > NIR] : < 2e-16
#>
#> Kappa : 0.9586
#>
#> Mcnemar's Test P-Value : 0.05183
#>
#> Sensitivity : 0.94568
#> Specificity : 0.99918
#> Pos Pred Value : 0.97455
#> Neg Pred Value : 0.99820
#> Prevalence : 0.03202
#> Detection Rate : 0.03028
#> Detection Prevalence : 0.03107
#> Balanced Accuracy : 0.97243
#>
#> 'Positive' Class : BT
#>
"10 Fold Results"
svm.radial.fit$resample #point est +/- std from 10 folds "variation in the third decimal place"...
svm.sd <- sd(svm.radial.fit[["resample"]][["Accuracy"]]*100)
#> [1] "10 Fold Results"
#> Accuracy Kappa sigma C Resample
#> 1 0.9944664 0.9107224 8.17509 0.25 Fold01
#> 2 0.9944664 0.9107224 8.17509 0.50 Fold01
#> 3 0.9952569 0.9225510 8.17509 1.00 Fold01
#> 4 0.9960474 0.9362303 8.17509 2.00 Fold01
#> 5 0.9960474 0.9362303 8.17509 4.00 Fold01
#> 6 0.9960474 0.9362303 8.17509 8.00 Fold01
#> 7 0.9968379 0.9483673 8.17509 16.00 Fold01
#> 8 0.9960474 0.9346692 8.17509 32.00 Fold01
#> 9 0.9944664 0.9085369 8.17509 64.00 Fold01
#> 10 0.9952569 0.9206316 8.17509 128.00 Fold01
#> 11 0.9905063 0.8372253 8.17509 0.25 Fold02
#> 12 0.9912975 0.8488696 8.17509 0.50 Fold02
#> 13 0.9912975 0.8488696 8.17509 1.00 Fold02
#> 14 0.9920886 0.8643544 8.17509 2.00 Fold02
#> 15 0.9920886 0.8643544 8.17509 4.00 Fold02
#> 16 0.9920886 0.8643544 8.17509 8.00 Fold02
#> 17 0.9920886 0.8643544 8.17509 16.00 Fold02
#> 18 0.9936709 0.8941728 8.17509 32.00 Fold02
#> 19 0.9936709 0.8967320 8.17509 64.00 Fold02
#> 20 0.9936709 0.8967320 8.17509 128.00 Fold02
#> 21 0.9960474 0.9346692 8.17509 0.25 Fold03
#> 22 0.9960474 0.9346692 8.17509 0.50 Fold03
#> 23 0.9952569 0.9206316 8.17509 1.00 Fold03
#> 24 0.9952569 0.9206316 8.17509 2.00 Fold03
#> 25 0.9952569 0.9206316 8.17509 4.00 Fold03
#> 26 0.9952569 0.9206316 8.17509 8.00 Fold03
#> 27 0.9952569 0.9206316 8.17509 16.00 Fold03
#> 28 0.9944664 0.9062417 8.17509 32.00 Fold03
#> 29 0.9944664 0.9062417 8.17509 64.00 Fold03
#> 30 0.9944664 0.9062417 8.17509 128.00 Fold03
#> 31 0.9952607 0.9243803 8.17509 0.25 Fold04
#> 32 0.9952607 0.9243803 8.17509 0.50 Fold04
#> 33 0.9952607 0.9243803 8.17509 1.00 Fold04
#> 34 0.9960506 0.9362319 8.17509 2.00 Fold04
#> 35 0.9960506 0.9362319 8.17509 4.00 Fold04
#> 36 0.9960506 0.9362319 8.17509 8.00 Fold04
#> 37 0.9960506 0.9362319 8.17509 16.00 Fold04
#> 38 0.9960506 0.9362319 8.17509 32.00 Fold04
#> 39 0.9944708 0.9107247 8.17509 64.00 Fold04
#> 40 0.9952607 0.9243803 8.17509 128.00 Fold04
#> 41 0.9976303 0.9608041 8.17509 0.25 Fold05
#> 42 0.9976303 0.9608041 8.17509 0.50 Fold05
#> 43 0.9976303 0.9608041 8.17509 1.00 Fold05
#> 44 0.9976303 0.9608041 8.17509 2.00 Fold05
#> 45 0.9984202 0.9741849 8.17509 4.00 Fold05
#> 46 0.9984202 0.9741849 8.17509 8.00 Fold05
#> 47 0.9984202 0.9741849 8.17509 16.00 Fold05
#> 48 0.9984202 0.9741849 8.17509 32.00 Fold05
#> 49 0.9984202 0.9741849 8.17509 64.00 Fold05
#> 50 0.9976303 0.9617392 8.17509 128.00 Fold05
#> 51 0.9976285 0.9617382 8.17509 0.25 Fold06
#> 52 0.9984190 0.9741842 8.17509 0.50 Fold06
#> 53 0.9984190 0.9741842 8.17509 1.00 Fold06
#> 54 0.9984190 0.9741842 8.17509 2.00 Fold06
#> 55 0.9984190 0.9741842 8.17509 4.00 Fold06
#> 56 0.9984190 0.9741842 8.17509 8.00 Fold06
#> 57 0.9976285 0.9608031 8.17509 16.00 Fold06
#> 58 0.9984190 0.9741842 8.17509 32.00 Fold06
#> 59 0.9984190 0.9741842 8.17509 64.00 Fold06
#> 60 0.9984190 0.9747928 8.17509 128.00 Fold06
#> 61 0.9960474 0.9330355 8.17509 0.25 Fold07
#> 62 0.9952569 0.9186234 8.17509 0.50 Fold07
#> 63 0.9968379 0.9470911 8.17509 1.00 Fold07
#> 64 0.9968379 0.9470911 8.17509 2.00 Fold07
#> 65 0.9960474 0.9346719 8.17509 4.00 Fold07
#> 66 0.9960474 0.9346719 8.17509 8.00 Fold07
#> 67 0.9976285 0.9608031 8.17509 16.00 Fold07
#> 68 0.9976285 0.9608031 8.17509 32.00 Fold07
#> 69 0.9984190 0.9741842 8.17509 64.00 Fold07
#> 70 0.9984190 0.9741842 8.17509 128.00 Fold07
#> 71 0.9968354 0.9457418 8.17509 0.25 Fold08
#> 72 0.9960443 0.9330281 8.17509 0.50 Fold08
#> 73 0.9960443 0.9330281 8.17509 1.00 Fold08
#> 74 0.9960443 0.9330281 8.17509 2.00 Fold08
#> 75 0.9960443 0.9330281 8.17509 4.00 Fold08
#> 76 0.9952532 0.9186126 8.17509 8.00 Fold08
#> 77 0.9944620 0.9062394 8.17509 16.00 Fold08
#> 78 0.9952532 0.9206296 8.17509 32.00 Fold08
#> 79 0.9936709 0.8914835 8.17509 64.00 Fold08
#> 80 0.9936709 0.8914835 8.17509 128.00 Fold08
#> 81 0.9960443 0.9330281 8.17509 0.25 Fold09
#> 82 0.9960443 0.9330281 8.17509 0.50 Fold09
#> 83 0.9960443 0.9330281 8.17509 1.00 Fold09
#> 84 0.9960443 0.9330281 8.17509 2.00 Fold09
#> 85 0.9968354 0.9470864 8.17509 4.00 Fold09
#> 86 0.9968354 0.9470864 8.17509 8.00 Fold09
#> 87 0.9968354 0.9470864 8.17509 16.00 Fold09
#> 88 0.9968354 0.9470864 8.17509 32.00 Fold09
#> 89 0.9968354 0.9483660 8.17509 64.00 Fold09
#> 90 0.9968354 0.9483660 8.17509 128.00 Fold09
#> 91 0.9984190 0.9747928 8.17509 0.25 Fold10
#> 92 0.9984190 0.9747928 8.17509 0.50 Fold10
#> 93 0.9984190 0.9747928 8.17509 1.00 Fold10
#> 94 0.9984190 0.9747928 8.17509 2.00 Fold10
#> 95 0.9984190 0.9747928 8.17509 4.00 Fold10
#> 96 0.9984190 0.9747928 8.17509 8.00 Fold10
#> 97 0.9984190 0.9747928 8.17509 16.00 Fold10
#> 98 0.9976285 0.9617382 8.17509 32.00 Fold10
#> 99 0.9984190 0.9747928 8.17509 64.00 Fold10
#> 100 0.9984190 0.9747928 8.17509 128.00 Fold10
The average accuracy across ten folds is 99.75 with a standard deviation of 0.191.
The final values used for the model were degree = 3, scale = 0.1 and C = 1.
| Method | KNN (k = 5) | LDA | QDA | Log. Regression | Random Forest (tuning param = ?) | SVM (tuning param = ?) |
|---|---|---|---|---|---|---|
| Accuracy | 99.75% | 98.5% | 99.46% | 99.56% | 99.97 | 99.75 |
| AUC | 99.98% | 98.88% | 99.71% | 99.85% | 99.5 | 99.96 |
| ROC | ||||||
| Threshold | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |
| Sensitivity | 95.8% | 80.99% | 83.46% | 89.38% | 99.01 | 94.57 |
| Specificity | 99.89% | 99.08% | 99.99% | 99.89% | 100 | 99.92 |
| FDR | 3.48% | 25.62% | 0.29% | 3.47% | 0 | 2.54 |
| Precision | 96.52% | 74.38% | 99.71% | 96.53% | 100 | 97.46 |
(discussion on FHO data why we do this… what the benefits are… potential pitfalls)
(discussion somewhere about ROC curves AUC and… other metrics)
#| Method | KNN (k = `r k_knn`) | LDA | QDA | Log. Regression | Random Forest (tuning param = ?) | SVM (tuning param = ?)|
#|-------------------------:|:--------------:|:---------:|:---------:|:---------------:|:--------------------------------:|:---------------------:|
#| Accuracy | `r acc_knn_FHO`% | `r acc_lda_FHO`% | `r acc_qda_FHO`% | `r acc_LR_FHO`% | `r acc_RF_FHO` | `r acc_SVM_FHO` |
#| AUC | `r auc_knn_FHO`% | `r auc_lda_FHO`% | `r auc_qda_FHO`% | `r auc_LR_FHO`% | `r auc_RF_FHO` | `r auc_SVM_FHO` |
#| ROC | | | | | | |
#| Threshold | `r thresh_knn_FHO` | `r thresh_lda_FHO` | `r thresh_qda_FHO` | `r thresh_LR_FHO` | `r thresh_RF_FHO` |`r thresh_SVM_FHO` |
#| Sensitivity=Recall=Power | `r sens_knn_FHO`% | `r sens_lda_FHO`% | `r sens_qda_FHO`% | `r sens_LR_FHO`% |`r sens_RF_FHO` | `r sens_SVM_FHO` |
#| Specificity=1-FPR | `r spec_knn_FHO`% | `r spec_lda_FHO`% | `r spec_qda_FHO`% | `r spec_LR_FHO`% |`r spec_RF_FHO` |`r spec_SVM_FHO` |
#| FDR | `r FDR_knn_FHO`% | `r FDR_lda_FHO`% | `r FDR_qda_FHO`% | `r FDR_LR_FHO`% | `r FDR_RF_FHO` |`r FDR_SVM_FHO` |
#| Precision=PPV | `r prec_knn_FHO`% | `r prec_lda_FHO`% | `r prec_qda_FHO`% | `r prec_LR_FHO`% |`r prec_RF_FHO` | `r prec_SVM_FHO` |
#consider if I was able to find an additional data source like lidar or infrared to pair with this dataset to improve model performance... ?
| LDA | QDA | |
|---|---|---|
| Assumptions | this is a lot of text what happens when you put this much text in this table | |
| Tuning Parameters |